The growth of cancerous tumors can be modeled by the Gompertz law N = -aN ln(bN), where N(t) is proportional to the number of cells in the tumor, and a, b are positive parameters.
(a) Interpret a and b biologcially
(b) Sketch the vector field and then graph N(t) for various initial values. (The predictions of this simple model agree surprisingly well with data on tumor growth as long as N is not too small).
(c) Using linear stability analysis, classify the fixed points of the Gompertz model.